Existence of rotating-periodic solutions for nonlinear second order vector differential equations

Abstract

In this paper, we establish two existence theorems of rotating-periodic solutions for nonlinear second order vector differential equations via the Leray-Schauder degree theory and the lower and upper solutions method. The concept "rotating-periodicity" is a kind of symmetry, which is a general version of periodicity, anti-periodicity, harmonic-periodicity, and it is also a special kind of quasi-periodicity. We also include several examples to illustrate the validity and applicability of our results.

Affine-Periodic Solutions for Newton systems

“…In [14], by using the lower and upper solution and the Leray-Schauder degree theory, Xu et al proved affine-periodic solutions to Newton affine-periodic systems. Zhang and Yang [17] investigated two existence theorems of rotating-periodic solutions for nonlinear second vector differential equations.…”